Get launched to the “magic integrating factor” and attempt utilizing it in a number of examples and functions.
Learn to cope with linear components, repeated linear components, and irreducible quadratic components.
See the right way to apply the alternating collection take a look at and use absolute worth.
File dimension: 13.83 GB
(video)
TGC – Understanding Calculus II: Issues, Options, and Tips
What Will You Be taught?
Get launched to the “magic integrating factor” and attempt utilizing it in a number of examples and functions.
Learn to cope with linear components, repeated linear components, and irreducible quadratic components.
See the right way to apply the alternating collection take a look at and use absolute worth.
Uncover the right way to categorical an arbitrary vector by way of the usual unit vector
Calculus II is the payoff for mastering Calculus I. This second course within the calculus sequence introduces you to thrilling new strategies and functions of one of the vital highly effective mathematical instruments ever invented. Outfitted with the talents of Calculus II, you’ll be able to resolve a big selection of issues within the bodily, organic, and social sciences, engineering, economics, and different areas. Success at Calculus II additionally offers you a strong basis for the additional research of arithmetic, and it meets the mathematics requirement for a lot of undergraduate majors.
However past these benefits, you will see that the strategies you study in Calculus II are sensible, attention-grabbing, and elegant, involving concepts which can be fantastically easy. As a result of it may possibly mannequin actual-life conditions, calculus has a tremendous vary of makes use of, and these functions come into full flower in Calculus II.
Understanding Calculus II: Issues, Options, and Tips takes you on this exhilarating journey in 36 intensively illustrated half-hour lectures that cowl all the foremost matters of the second full-yr calculus course in highschool on the Faculty Board Superior Placement BC stage or a second-semester course in faculty. Drawing on a long time of instructing expertise, Professor Bruce H. Edwards of the College of Florida enriches his lectures with crystal-clear explanations, frequent research ideas, pitfalls to keep away from, and—better of all—lots of of examples and follow issues which can be particularly designed to clarify and reinforce key ideas.
Few calculus lecturers are as certified, accessible, or entertaining as Professor Edwards, who has received a number of instructing awards and coauthored a finest-promoting collection of calculus textbooks. Many calculus college students quit making an attempt to grasp why a specific process works and resort to memorizing the steps to an answer. With Professor Edwards, the underlying ideas are at all times clear and consistently bolstered, which tremendously eases the trail to studying the fabric.
Get behind the Wheel of the “Limit Machine”
Professor Edwards begins with a 3-lecture overview of the basic concepts of calculus. He additionally consists of transient evaluations of main ideas all through the course, which makes Understanding Calculus II a self-contained lecture collection for anybody who’s already conversant in the 2 essential operations of calculus, differentiation and integration. Professor Edwards takes these concepts past the definitions, guidelines, and formulation which can be the main focus of first-semester calculus and applies them in intriguing methods. For instance:
Differential equations: This far-reaching subject places derivatives to work—modeling inhabitants progress, nuclear decay, falling objects, and numerous different processes involving change. Professor Edwards remembers that as a younger mathematician, he spent summers working for NASA, fixing differential equations for plane in flight.
Infinite collection: Does including an infinite sequence of numbers give an infinite consequence? Not essentially. The collection could converge on a selected worth, or it could diverge to infinity. Calculus can present the reply for various kinds of infinite collection and symbolize acquainted capabilities from algebra or trigonometry in shocking methods.
Vectors: Among the many geometric functions of calculus is the evaluation of vectors. These are portions, resembling velocity, which have each magnitude and course. In Calculus II, you study strategies for evaluating vectors within the aircraft, permitting you to unravel issues involving transferring and accelerating objects, whether or not they’re on a straight or curved path.
Understanding Calculus II covers the above topics in appreciable depth, significantly infinite collection, which you discover in 11 lectures. You additionally research different normal matters in second-semester calculus, together with
integration formulation and strategies,
integrating areas and volumes,
Taylor and Maclaurin polynomials,
L’Hôpital’s rule for evaluating limits,
evaluating improper integrals,
calculus utilized to parametric equations, and
calculus utilized to polar coordinates.
These very completely different functions of calculus every contain the important thought of the restrict. Professor Edwards notes that calculus might be considered a “limit machine”—a set of procedures for approaching infinitely near a price. One of many attention-grabbing options of calculus is its logical rigor mixed with its inventive use of the mysterious entity of the infinite. From this uncommon marriage emerge astonishingly exact options to in any other case inaccessible issues.
Discover the Immense Riches of Calculus
Calculus is stuffed with fascinating properties, baffling paradoxes, and entertaining issues. Among the many many you examine in Understanding Calculus II are these:
Gabriel’s Horn: Rotate a easy curve round its axis and you get a 3-dimensional form that appears like an infinitely lengthy trumpet. Referred to as Gabriel’s Horn, this geometric determine has an uncommon property: It has infinite floor space however finite quantity. See calculus show that this should be so.
Baseball thriller: A baseball 3 toes above house plate is hit at 100 toes per second and at an angle of 45 levels. Make use of Newton’s second regulation of movement and the spinoff of the place perform to find out if the ball will likely be a house run, clearing a ten-foot-excessive fence 300 toes away.
Cantor Set: Take away the center third of a line section. Repeat with the 2 items that stay. Repeat once more advert infinitum. The tip factors of all of the items will type an infinite set. However what in regards to the whole size of all the road segments? Summing this infinite collection reveals the shocking reply.
Grasp Calculus on Your Personal Schedule
Understanding Calculus II is an immensely rewarding expertise which you can research at your personal tempo. Professor Edwards typically encourages you to pause the video and take a look at your self by fixing an issue earlier than he reveals the reply. Those that will profit from this participating and versatile presentation embody:
highschool or faculty college students at present, or about to be, enrolled in Calculus II who need private teaching from an impressive instructor;
highschool college students getting ready for the Faculty Board Superior Placement take a look at in Calculus on the BC stage;
college students in increased-stage math programs or professionals who need a rigorous overview of calculus; and
anybody concerned with pursuing one in all life’s biggest mental adventures, which has been fixing tough issues for over 300 years.
A 3-time Trainer of the Yr on the College of Florida, Professor Edwards is aware of the right way to assist college students surmount the hindrances on their path to mastering calculus. On this course, he makes use of a gentle stream of on-display screen equations, graphs, and different visible aids to doc the important thing steps in fixing pattern issues. The accompanying workbook is designed to strengthen every lecture with extra follow issues and labored-out options, in addition to lecture summaries, ideas, and pitfalls; and formulation for derivatives, integration, and energy collection.
Professor Edwards’s lectures additionally embody a function he calls “You Be the Teacher,” wherein he reverses roles, difficult you to reply a typical query posed within the classroom, design an acceptable downside for example a precept, or in any other case put your self within the teacher’s footwear—a useful train in studying to assume for your self within the language of calculus.
Open Doorways with Your New Fluency
The place of calculus on the finish of the highschool math curriculum makes it look like a last vacation spot. However it is usually solely a starting. Calculus is a world unto itself, an ever-increasing assortment of instruments that may resolve probably the most intractable issues in ingenious and typically shocking methods. The deeper you go into calculus, the richer it will get and the higher you are ready for much more superior math programs that open doorways of their very own.
In his final lecture, Professor Edwards seems forward to the place your math research could take you after this course. It’s thrilling terrain. Think about arriving out of the country geared up with the flexibility to talk the nation’s language. Your alternatives for exploration, interplay, and additional studying are nearly limitless. That’s what Understanding Calculus II does on your fluency in one of many biggest achievements of the human thoughts.
36 lectures
| Common 31 minutes every
1Basic Features of Calculus and Limits
2 Differentiation Heat-up
3Integration Heat-up
4Differential Equations—Development and Decay
5Applications of Differential Equations
6Linear Differential Equations
7Areas and Volumes
8Arc Size, Floor Space, and Work
9Moments, Facilities of Mass, and Centroids
10Integration by Elements
11Trigonometric Integrals
12Integration by Trigonometric Substitution
13Integration by Partial Fractions
14Indeterminate Types and L’Hôpital’s Rule
15Improper Integrals
16Sequences and Limits
17Infinite Collection—Geometric Collection
18Series, Divergence, and the Cantor Set
19Integral Check—Harmonic Collection, p-Collection
20The Comparability Assessments
21Alternating Collection
Having developed checks for constructive-time period collection, flip to collection having phrases that alternate between constructive and destructive. See the right way to apply the alternating collection take a look at. Then use absolute worth to have a look at the ideas of conditional and absolute convergence for collection with constructive and destructive phrases.
22The Ratio and Root Assessments
23Taylor Polynomials and Approximations
24Power Collection and Intervals of Convergence
25Representation of Features by Energy Collection
26Taylor and Maclaurin Collection
27Parabolas, Ellipses, and Hyperbolas
28Parametric Equations and the Cycloid
29Polar Coordinates and the Cardioid
30Area and Arc Size in Polar Coordinates
31Vectors within the Aircraft
32The Dot Product of Two Vectors
33Vector-Valued Features
34Velocity and Acceleration
35Acceleration’s Tangent and Regular Vectors
36Curvature and the Most Bend of a Curve
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